Many nonlinear systems that depend on both current and past data use Volterra series in their control apparatus. The coefficients that define the Volterra series are typically generated during a training phase and then applied to the control apparatus to control the processing of the actual data. The calculation of the coefficients presents computational challenges that make them difficult to implement for adaptive control of the nonlinear systems that calculate coefficients on the fly.
One such nonlinear system is a power amplifier used in communication equipments. These power amplifiers may generate distortion in adjacent frequency bands due to nonlinearities in the amplifier transfer functions. When the amplified signal has a relatively low bandwidth, the distortion caused by these nonlinearities can be corrected using a non-linear model that does not take into account any memory effects of the amplifier. As bandwidth increases, however, these memory effects become more significant. One way to reduce distortion is to change the operating point of the amplifier so that it is within a linear region of the amplifier transfer function. This technique, however, undesirably reduces both the power output and/or the efficiency of the amplifier. Digital predistortion systems for amplifiers processing wideband signals used in present and future communication systems employ predistortion models based on Volterra series that take into account the memory effects of the power amplifiers.